# Please submit problems in the comment section. Try to make the statement as close to the actual statement as possible.

Our team will upload the solutions. Problems are contributed by students.

# Problems

1. Suppose $$\frac{8^x + 27^x}{12^x + 18 ^x} = 7/6$$. Find x.

2. There is a parallelogram ABCD. O is any point in the interior such that angle AOB + angle DOC = 180. Prove that angle ODC= angle OBC

3. Find the number of natural number n for which $$n^6+n^4+1$$ is a perfect square

4. $$\phi_k (m) = \phi_1 (\phi_{k-1} (m))$$ and $$\phi_1 (m)$$ is number of divisors of m . Find k for which $$\phi_k (2019^2019) =2$$

5. If there exists a calculator with 12 buttons, 10 being the buttons for the digits and A and B being two buttons being processes where if n is displayed on the calculator if A is pressed it increases the displayed number by 1 and if B is pressed it multiplies n by 2 hence 2n. Hence find the minimum number of moves to get 260 from 1

6. Find the sum 1+111+11111+1111111+…..1….111(2k+1) ones

# Objective Section (Answer Key)

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# Faculty Team (for this section) #### Ashani Dasgupta

Founder – Faculty at Cheenta.

Pursuing Ph.D. at University of Wisconsin, Milwaukee. USA

Research Interest: Geometric Group Theory #### Srijit Mukherjee

Faculty – Admin at Cheenta

Pursuing B.Stat at Indian Statistical Institute, India #### Writabrata Bhattacharya

Faculty at Cheenta

Pursuing B.Sc. Math at Chennai Mathematical Institute, India

Research Interest – Algebraic Geometry #### Ishan Sengupta

Associate Faculty at Cheenta

Pursuing B.Stat from Indian Statistical Institute, India